Broken Symmetry Approach to Magnetic Properties of Oligonuclear Transition-Metal Complexes: Application to Hyperfine Tensors of Mixed-Valence Manganese Compounds

摘要

The broken symmetry method is a standard approach for the calculation of isotropic exchange coupling constants in oligonuclear transition-metal compounds with density functional methods. It is most transparently derived through a mapping approach, where one maps energies calculated for broken symmetry configurations to the expectation value of Ising-type wave functions with a spin Hamiltonian. This approach is generalized to the anisotropic case, targeted at the calculation of zero-field splitting, g matrices, and hyperfine A tensors. Local quantities can be extracted from density functional calculations, which then give the final results by performing a spin projection through an exact diagonalization of a spin Hamiltonian. It is demonstrated how to do this within the strong exchange limit and beyond. In the case of hyperfine A tensors, more local quantities (on-site and off-site tensors) arise than treated in methods described so far. The importance of these off-site tensors in the hyperfine case is demonstrated in two pilot applications to mixed-valence manganese complexes (DTNE and a CaMn_(4) model for the S _(2) state of the oxygen-evolving center of photosystem II) that have already been studied using density functional methods.